theorem :: TOPDIM_2:6

for n being Nat
for TM being metrizable TopSpace st TM is second-countable & TM is finite-ind & ind TM <= n holds
ex A, B being Subset of TM st
( [#] TM = A \/ B & A misses B & ind A <= n - 1 & ind B <= 0 ) by Lm3;